Quote:
Originally Posted by Moontanman
Is time really the fourth dimension? If a 6" line has an infinite number of points, and a 6" square contains an infinite number of 6" lines and a 6" cube has an infinite number of 6" squares doesn't it follow that a 6" hypercube has to have an infinite number of 6" cubes?
|
Assuming that your coordinate space were using the Reals {R}, then yes, there would be
an infinite number of 6" cubes (uncountably so) within the hypercube. In fact for any number
of dimensions, there are an (uncountable) number of subspace objects (1-dimension lower)
within a given object for some space of dimension n. This is a property of the group
GL(g, n) for vector spaces.
Quote:
Originally Posted by Moontanman
Does this analogy hold up to our idea of time? I don't think so, could time have nothing to do with dimensions, could it be a process, not a thing?
|
Your example above was a representation. Time as expressed in 4-d space {x,y,z,t}
is a representation. The value (coordinate) t is arbitrary. As such (using Reals) is
also uncountably infinite.
An important point here is we are currently speaking Mathematically and "Classically".
From the point-of-view (POV) of QM where coordinates can be discrete ("quantized"),
this can still be a large number yet finitely divisible. This would be so for time as has
recently been conjectured.
As representations go, time is not exactly the same as a space coordinate yet can be
transformed into one by multiplying c (velocity of light).
maddog
